Histogram Equalization {#tutorial_histogram_equalization}
======================

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Goal
----

In this tutorial you will learn:

-   What an image histogram is and why it is useful
-   To equalize histograms of images by using the OpenCV function @ref cv::equalizeHist

Theory
------

### What is an Image Histogram?

-   It is a graphical representation of the intensity distribution of an image.
-   It quantifies the number of pixels for each intensity value considered.

![](images/Histogram_Equalization_Theory_0.jpg)

### What is Histogram Equalization?

-   It is a method that improves the contrast in an image, in order to stretch out the intensity
    range (see also the corresponding <a href="https://en.wikipedia.org/wiki/Histogram_equalization">Wikipedia entry</a>).
-   To make it clearer, from the image above, you can see that the pixels seem clustered around the
    middle of the available range of intensities. What Histogram Equalization does is to *stretch
    out* this range. Take a look at the figure below: The green circles indicate the
    *underpopulated* intensities. After applying the equalization, we get an histogram like the
    figure in the center. The resulting image is shown in the picture at right.

![](images/Histogram_Equalization_Theory_1.jpg)

### How does it work?

-   Equalization implies *mapping* one distribution (the given histogram) to another distribution (a
    wider and more uniform distribution of intensity values) so the intensity values are spread
    over the whole range.
-   To accomplish the equalization effect, the remapping should be the *cumulative distribution
    function (cdf)* (more details, refer to *Learning OpenCV*). For the histogram \f$H(i)\f$, its
    *cumulative distribution* \f$H^{'}(i)\f$ is:

    \f[H^{'}(i) = \sum_{0 \le j < i} H(j)\f]

    To use this as a remapping function, we have to normalize \f$H^{'}(i)\f$ such that the maximum value
    is 255 ( or the maximum value for the intensity of the image ). From the example above, the
    cumulative function is:

    ![](images/Histogram_Equalization_Theory_2.jpg)

-   Finally, we use a simple remapping procedure to obtain the intensity values of the equalized
    image:

    \f[equalized( x, y ) = H^{'}( src(x,y) )\f]

Code
----

-   **What does this program do?**
    -   Loads an image
    -   Convert the original image to grayscale
    -   Equalize the Histogram by using the OpenCV function @ref cv::equalizeHist
    -   Display the source and equalized images in a window.

@add_toggle_cpp
-   **Downloadable code**: Click
    [here](https://github.com/opencv/opencv/tree/master/samples/cpp/tutorial_code/Histograms_Matching/EqualizeHist_Demo.cpp)

-   **Code at glance:**
    @include samples/cpp/tutorial_code/Histograms_Matching/EqualizeHist_Demo.cpp
@end_toggle

@add_toggle_java
-   **Downloadable code**: Click
    [here](https://github.com/opencv/opencv/tree/master/samples/java/tutorial_code/Histograms_Matching/histogram_equalization/EqualizeHistDemo.java)

-   **Code at glance:**
    @include samples/java/tutorial_code/Histograms_Matching/histogram_equalization/EqualizeHistDemo.java
@end_toggle

@add_toggle_python
-   **Downloadable code**: Click
    [here](https://github.com/opencv/opencv/tree/master/samples/python/tutorial_code/Histograms_Matching/histogram_equalization/EqualizeHist_Demo.py)

-   **Code at glance:**
    @include samples/python/tutorial_code/Histograms_Matching/histogram_equalization/EqualizeHist_Demo.py
@end_toggle

Explanation
-----------

-   Load the source image:

    @add_toggle_cpp
    @snippet samples/cpp/tutorial_code/Histograms_Matching/EqualizeHist_Demo.cpp Load image
    @end_toggle

    @add_toggle_java
    @snippet samples/java/tutorial_code/Histograms_Matching/histogram_equalization/EqualizeHistDemo.java Load image
    @end_toggle

    @add_toggle_python
    @snippet samples/python/tutorial_code/Histograms_Matching/histogram_equalization/EqualizeHist_Demo.py Load image
    @end_toggle

-   Convert it to grayscale:

    @add_toggle_cpp
    @snippet samples/cpp/tutorial_code/Histograms_Matching/EqualizeHist_Demo.cpp Convert to grayscale
    @end_toggle

    @add_toggle_java
    @snippet samples/java/tutorial_code/Histograms_Matching/histogram_equalization/EqualizeHistDemo.java Convert to grayscale
    @end_toggle

    @add_toggle_python
    @snippet samples/python/tutorial_code/Histograms_Matching/histogram_equalization/EqualizeHist_Demo.py Convert to grayscale
    @end_toggle

-   Apply histogram equalization with the function @ref cv::equalizeHist :

    @add_toggle_cpp
    @snippet samples/cpp/tutorial_code/Histograms_Matching/EqualizeHist_Demo.cpp Apply Histogram Equalization
    @end_toggle

    @add_toggle_java
    @snippet samples/java/tutorial_code/Histograms_Matching/histogram_equalization/EqualizeHistDemo.java Apply Histogram Equalization
    @end_toggle

    @add_toggle_python
    @snippet samples/python/tutorial_code/Histograms_Matching/histogram_equalization/EqualizeHist_Demo.py Apply Histogram Equalization
    @end_toggle
    As it can be easily seen, the only arguments are the original image and the output (equalized)
    image.

-   Display both images (original and equalized):

    @add_toggle_cpp
    @snippet samples/cpp/tutorial_code/Histograms_Matching/EqualizeHist_Demo.cpp Display results
    @end_toggle

    @add_toggle_java
    @snippet samples/java/tutorial_code/Histograms_Matching/histogram_equalization/EqualizeHistDemo.java Display results
    @end_toggle

    @add_toggle_python
    @snippet samples/python/tutorial_code/Histograms_Matching/histogram_equalization/EqualizeHist_Demo.py Display results
    @end_toggle

-   Wait until user exists the program

    @add_toggle_cpp
    @snippet samples/cpp/tutorial_code/Histograms_Matching/EqualizeHist_Demo.cpp Wait until user exits the program
    @end_toggle

    @add_toggle_java
    @snippet samples/java/tutorial_code/Histograms_Matching/histogram_equalization/EqualizeHistDemo.java Wait until user exits the program
    @end_toggle

    @add_toggle_python
    @snippet samples/python/tutorial_code/Histograms_Matching/histogram_equalization/EqualizeHist_Demo.py Wait until user exits the program
    @end_toggle

Results
-------

-#  To appreciate better the results of equalization, let's introduce an image with not much
    contrast, such as:

    ![](images/Histogram_Equalization_Original_Image.jpg)

    which, by the way, has this histogram:

    ![](images/Histogram_Equalization_Original_Histogram.jpg)

    notice that the pixels are clustered around the center of the histogram.

-#  After applying the equalization with our program, we get this result:

    ![](images/Histogram_Equalization_Equalized_Image.jpg)

    this image has certainly more contrast. Check out its new histogram like this:

    ![](images/Histogram_Equalization_Equalized_Histogram.jpg)

    Notice how the number of pixels is more distributed through the intensity range.

@note
Are you wondering how did we draw the Histogram figures shown above? Check out the following
tutorial!
